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# Calculus Examples

Step 1

Differentiate using the Quotient Rule which states that is where and .

Step 2

By the Sum Rule, the derivative of with respect to is .

Step 3

The derivative of with respect to is .

Step 4

Step 4.1

Since is constant with respect to , the derivative of with respect to is .

Step 4.2

Add and .

Step 4.3

By the Sum Rule, the derivative of with respect to is .

Step 4.4

Differentiate using the Power Rule which states that is where .

Step 4.5

Since is constant with respect to , the derivative of with respect to is .

Step 4.6

Simplify the expression.

Step 4.6.1

Add and .

Step 4.6.2

Multiply by .

Step 5

Step 5.1

Apply the distributive property.

Step 5.2

Simplify the numerator.

Step 5.2.1

Simplify each term.

Step 5.2.1.1

Multiply by .

Step 5.2.1.2

Multiply .

Step 5.2.1.2.1

Multiply by .

Step 5.2.1.2.2

Multiply by .

Step 5.2.2

To write as a fraction with a common denominator, multiply by .

Step 5.2.3

Combine and .

Step 5.2.4

Combine the numerators over the common denominator.

Step 5.2.5

Simplify each term.

Step 5.2.5.1

Simplify the numerator.

Step 5.2.5.1.1

Apply the distributive property.

Step 5.2.5.1.2

Multiply by .

Step 5.2.5.1.3

Reorder terms.

Step 5.2.5.1.4

Rewrite in a factored form.

Step 5.2.5.1.4.1

Regroup terms.

Step 5.2.5.1.4.2

Factor out of .

Step 5.2.5.1.4.2.1

Reorder and .

Step 5.2.5.1.4.2.2

Factor out of .

Step 5.2.5.1.4.2.3

Factor out of .

Step 5.2.5.1.4.2.4

Factor out of .

Step 5.2.5.1.4.2.5

Factor out of .

Step 5.2.5.1.4.2.6

Factor out of .

Step 5.2.5.1.4.2.7

Rewrite as .

Step 5.2.5.1.4.3

Reorder terms.

Step 5.2.5.1.4.4

Factor out of .

Step 5.2.5.1.4.4.1

Reorder and .

Step 5.2.5.1.4.4.2

Rewrite as .

Step 5.2.5.1.4.4.3

Factor out of .

Step 5.2.5.1.4.4.4

Rewrite as .

Step 5.2.5.1.4.5

Reorder terms.

Step 5.2.5.2

Move the negative in front of the fraction.

Step 5.2.6

To write as a fraction with a common denominator, multiply by .

Step 5.2.7

To write as a fraction with a common denominator, multiply by .

Step 5.2.8

Write each expression with a common denominator of , by multiplying each by an appropriate factor of .

Step 5.2.8.1

Multiply by .

Step 5.2.8.2

Multiply by .

Step 5.2.8.3

Reorder the factors of .

Step 5.2.9

Combine the numerators over the common denominator.

Step 5.2.10

Simplify the numerator.

Step 5.2.10.1

Apply the distributive property.

Step 5.2.10.2

Simplify.

Step 5.2.10.2.1

Multiply .

Step 5.2.10.2.1.1

Multiply by .

Step 5.2.10.2.1.2

Multiply by .

Step 5.2.10.2.2

Multiply by .

Step 5.2.10.3

Apply the distributive property.

Step 5.2.10.4

Simplify.

Step 5.2.10.4.1

Multiply by .

Step 5.2.10.4.2

Move to the left of .

Step 5.2.10.4.3

Multiply by .

Step 5.2.10.4.4

Multiply by .

Step 5.2.10.5

Apply the distributive property.

Step 5.2.10.6

Multiply by .

Step 5.2.10.7

Reorder terms.

Step 5.2.11

Factor out of .

Step 5.2.12

Factor out of .

Step 5.2.13

Factor out of .

Step 5.2.14

Factor out of .

Step 5.2.15

Factor out of .

Step 5.2.16

Rewrite as .

Step 5.2.17

Factor out of .

Step 5.2.18

Factor out of .

Step 5.2.19

Factor out of .

Step 5.2.20

Factor out of .

Step 5.2.21

Factor out of .

Step 5.2.22

Rewrite as .

Step 5.2.23

Move the negative in front of the fraction.

Step 5.3

Combine terms.

Step 5.3.1

Rewrite as a product.

Step 5.3.2

Multiply by .

Step 5.3.3

Move to the left of .